Given a line with a slope of infinite (g(x)=infinite*x) and a parabola (f(x)=x^2)... are they a secant or a tangent?
Since the g(x) is going straight up they will only cross once at (0|0), they should count as a tangent but it it is still crossing it which would make it a secant? Is there any way of calculating this?
Vertical lines have equations of the form $x=c$, not the usual slope-intercept form.
I presume you mean the line $x=0$ (the vertical line through the origin). This is not a tangent line for the curve $y=x^2$ at $(0,0)$. The tangent line at that point is actually horizontal, so it is $y=0x+0$, or just $y=0$.
So your vertical line is secant, not tangent.
Tangents "graze" the curve; they represent the straight line that best matches the "direction" of the curve at a given point.